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A153177
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a(n) = L(9n)/L(n) where L(n) = Lucas number A000204(n).
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3
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76, 1926, 109801, 4769326, 230701876, 10716675201, 505618944676, 23714405408926, 1114769987764201, 52357935173823126, 2459933168462154076, 115560463558534156801, 5428954301161174383676, 255043991670277234750326
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| All numbers in this sequence are:
congruent to 1 mod 100 (iff n is congruent to 0 mod 3)
congruent to 26 mod 100 (iff n is congruent to 2 or 4 mod 6),
congruent to 76 mod 100 (iff n is congruent to 1 or 5 mod 6).
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (34,714,-4641,-12376,12376,4641,-714,-34,1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 22 2010]
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FORMULA
| a(n)= +34*a(n-1) +714*a(n-2) -4641*a(n-3) -12376*a(n-4) +12376*a(n-5) +4641*a(n-6) -714*a(n-7) -34*a(n-8) +a(n-9). G.f.: -x*(76-658*x-9947*x^2+13644*x^3+26020*x^4-5306*x^5-1372*x^6+42*x^7+x^8) / ( (x-1)*(x^2+18*x+1)*(x^2-47*x+1)*(x^2+3*x+1)*(x^2-7*x+1) ). a(n) = 1-(-1)^n*A087215(n) -(-1)^n*A005248(n) +A056854(n) +A087265(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 22 2010]
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MATHEMATICA
| Table[LucasL[9 n]/LucasL[n], {n, 1, 150}]
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CROSSREFS
| A000032, A000204, A110391, A153173, A153175.
Cf. A153179, A153180. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 22 2010]
Sequence in context: A185819 A060190 A156399 * A166191 A188400 A205918
Adjacent sequences: A153174 A153175 A153176 * A153178 A153179 A153180
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KEYWORD
| nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Dec 20 2008
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